In this paper, we ask if Navier Stokes equation will provide the correct description of the data from MD simulations in two and three dimensions. To do so, we do DNS of the continuity equations for mass, momentum and energy using the same numerical methods followed in Ref. [1]}. In continuation of our earlier work [2]}, [3]}, steric effects, which are absent in one-dimensional systems, were included by modifying the equation of state that relates pressure to temperature and density from the ideal gas equation of state to the virial equation of state.
The boundary conditions for the equations in radial coordinates are obtained from DNS of the equations in cartesian coordinates. The constants related to heat conduction and viscosity are determined from kinetic theory. We then show that the results from DNS match the data from MD simulations without any fitting parameter in two dimensions. In three dimensions, there is a small mismatch which is resolved by treating the constants appearing in heat conduction and viscosity terms as free parameters. We conclude that to obtain the correct description of a blast wave in the hydrodynamic regime, the solution has to be first found for the Navier Stokes equation, which includes heat conduction and viscosity terms, followed by taking the appropriate scaling limit.
